SOLUTION: The value of a car after t years can be found using the formula V = C(1 - r)t, where V is the current value of the car, C is the original price of the car, and r is the rate of dep

Question 972858: The value of a car after t years can be found using the formula V = C(1 - r)t, where V is the current value of the car, C is the original price of the car, and r is the rate of depreciation.
Solve the formula for r .
Raj bought a car 4.5 years ago for $25,000, and the current value of the car is $12,000. At what percentage rate has the car depreciated? Round your answer to the nearest whole number.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
V=C(1-r)^t (raise it to the t power)
12,000=25,000(1-r)^4.5

12000=25000(1-r)^4.5
(12000/25000) = (1-r)^4.5
0.48=(1-r)^4.5
logs of both sides
log 0.48= -0.319=4.5 log (1-r)
(-0.319/4.5)=
-.0701=log(1-r)
Now raise each to the 10 power
0.8495=1-r
r= 0.1505 or 15.05%
(1-r)^4.5=0.48, and that is the ratio between the present and original value.

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